Fitting PD-NEUT-TOF Si-SEPD¶

This example shows how to refine the crystal structure parameters of Si from neutron diffraction data in a time-of-flight experiment performed on SEPD diffractometer at Argonne.

Import¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

Job¶

Create a job — the main object to store all the information

In [3]:

job = ed.Job(type='tof')

job = ed.Job(type='tof')

Model¶

Create a phase object

In [4]:

phase = ed.Phase(name='si')

phase = ed.Phase(name='si')

Set space group

In [5]:

phase.space_group.name_hm_alt = 'F d -3 m'

phase.space_group.name_hm_alt = 'F d -3 m'

Set cell parameters

In [6]:

phase.cell.length_a = 5.43146

phase.cell.length_a = 5.43146

Add atoms

In [7]:

phase.atom_sites.append(label='Si', 
                        type_symbol='Si', 
                        fract_x=0, 
                        fract_y=0, 
                        fract_z=0, 
                        occupancy=1,
                        b_iso_or_equiv=0.529)

phase.atom_sites.append(label='Si', type_symbol='Si', fract_x=0, fract_y=0, fract_z=0, occupancy=1, b_iso_or_equiv=0.529)

Add phase to the job object

In [8]:

job.add_phase(phase=phase)
print(job.phases)

job.add_phase(phase=phase) print(job.phases)

Several values of it_coordinate_system_code have been defined:
2, 1
The default value has been choosen:'2'.
Several values of it_coordinate_system_code have been defined:
2, 1
The default value has been choosen:'2'.
Collection of 1 phases: ['si']

Show phase info in CIF format

In [9]:

phase = job.phases['si']
print(phase.cif)

phase = job.phases['si'] print(phase.cif)

data_si
_cell_length_a 5.43146
_cell_length_b 5.43146
_cell_length_c 5.43146
_cell_angle_alpha 90.00000000
_cell_angle_beta 90.00000000
_cell_angle_gamma 90.00000000
_space_group_name_H-M_ref 'F d -3 m'
_space_group_IT_coordinate_system_code 1

loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_occupancy
_atom_site_adp_type
_atom_site_B_iso_or_equiv
Si Si 0.00000000 0.00000000 0.00000000 1.00000000 Biso 0.529

Display the crystal structure of a given model

In [10]:

job.show_crystal_structure(id='si')

job.show_crystal_structure(id='si')

You appear to be running in JupyterLab (or JavaScript failed to load for some other reason). You need to install the 3dmol extension:
jupyter labextension install jupyterlab_3dmol

Experiment¶

Load experimentally measured data from a file in XYE format

In [11]:

job.add_experiment_from_file('data/sepd.xye')

job.add_experiment_from_file('data/sepd.xye')

Display the experimentally measured data

In [12]:

job.show_experiment_chart()

job.show_experiment_chart()

Define a point background

In [13]:

background_points = [(x, 200) for x in range(0, 35000, 5000)]
print(background_points)

background_points = [(x, 200) for x in range(0, 35000, 5000)] print(background_points)

[(0, 200), (5000, 200), (10000, 200), (15000, 200), (20000, 200), (25000, 200), (30000, 200)]

In [14]:

job.set_background(background_points)

job.set_background(background_points)

Display the experiment chart after setting the background

In [15]:

job.show_experiment_chart()

job.show_experiment_chart()

Analysis¶

Display the analysis chart before setting initial parameter values

In [16]:

job.show_analysis_chart()

job.show_analysis_chart()

Create aliases for the two types of experimental parameters

In [17]:

pattern_params = job.pattern
experiment_params = job.parameters

pattern_params = job.pattern experiment_params = job.parameters

Change the default value of some instrumental parameters and display the analysis chart again

In [18]:

experiment_params.dtt1 = 7476.91
experiment_params.dtt2 = -1.54
experiment_params.ttheta_bank = 144.845
job.show_analysis_chart()

experiment_params.dtt1 = 7476.91 experiment_params.dtt2 = -1.54 experiment_params.ttheta_bank = 144.845 job.show_analysis_chart()

Change the scale and display the analysis chart again

In [19]:

phase.scale = 10
job.show_analysis_chart()

phase.scale = 10 job.show_analysis_chart()

Change the default values of the peak profile related parameters and display the analysis chart again

In [20]:

experiment_params.alpha0 = 0.024
experiment_params.alpha1 = 0.204
experiment_params.beta0 = 0.038
experiment_params.beta1 = 0.011
experiment_params.sigma0 = 0.0
experiment_params.sigma1 = 0.0
experiment_params.sigma2 = 0.0
job.show_analysis_chart()

experiment_params.alpha0 = 0.024 experiment_params.alpha1 = 0.204 experiment_params.beta0 = 0.038 experiment_params.beta1 = 0.011 experiment_params.sigma0 = 0.0 experiment_params.sigma1 = 0.0 experiment_params.sigma2 = 0.0 job.show_analysis_chart()

Select parameters to be refined in the first round

In [21]:

phase.scale.free = True
pattern_params.zero_shift.free = True

phase.scale.free = True pattern_params.zero_shift.free = True

Print parameters to be refined (free parameters) before fitting

In [22]:

job.print_free_parameters()

job.print_free_parameters()

Out[22]:

	names	values	errors	units
1	scale	10.0	0.0

Start Least-Squares minimization to refine the selected parameters

In [23]:

job.fit()

job.fit()

Fitting successful
Duration: 6.56 s
Reduced chi: 36.80

Print the refined parameters after fitting

In [24]:

job.print_free_parameters()

job.print_free_parameters()

Out[24]:

	names	values	errors	units
1	scale	12.810954	0.112699
2	zero_shift	-4.166396	0.052262	µs

Display the analysis chart after the first fitting

In [25]:

job.show_analysis_chart()

job.show_analysis_chart()

Allow background parameters to be refined

In [26]:

for background_point in pattern_params.backgrounds[0]:
    background_point.y.free = True

for background_point in pattern_params.backgrounds[0]: background_point.y.free = True

Print free parameters before the second fitting

In [27]:

job.print_free_parameters()

job.print_free_parameters()

Out[27]:

	names	values	errors	units
1	scale	12.810954	0.112699
2	zero_shift	-4.166396	0.052262	µs
3	intensity	200.000000	0.000000
4	intensity	200.000000	0.000000
5	intensity	200.000000	0.000000
6	intensity	200.000000	0.000000
7	intensity	200.000000	0.000000
8	intensity	200.000000	0.000000
9	intensity	200.000000	0.000000

Start second round of minimization

In [28]:

job.fit()

job.fit()

Fitting successful
Duration: 5.04 s
Reduced chi: 16.18

Print free parameters after the second fitting

In [29]:

job.print_free_parameters()

job.print_free_parameters()

Out[29]:

	names	values	errors	units
1	scale	13.169738	0.075010
2	zero_shift	-4.165397	0.033715	µs
3	intensity	269.666225	7.992930
4	intensity	150.600340	2.523188
5	intensity	121.156660	1.990883
6	intensity	136.251201	1.988307
7	intensity	133.911792	1.974323
8	intensity	175.057849	2.293309
9	intensity	183.334800	3.224987

Display the analysis chart after the second fitting

In [30]:

job.show_analysis_chart()

job.show_analysis_chart()

Select more parameters to be refined in the third round

In [31]:

experiment_params.sigma0.free = True
experiment_params.sigma1.free = True
experiment_params.sigma2.free = True

experiment_params.sigma0.free = True experiment_params.sigma1.free = True experiment_params.sigma2.free = True

Disable refinement of background parameters

In [32]:

for background_point in pattern_params.backgrounds[0]:
    background_point.y.free = False

for background_point in pattern_params.backgrounds[0]: background_point.y.free = False

Print free parameters before the third fitting

In [33]:

job.print_free_parameters()

job.print_free_parameters()

Out[33]:

	names	values	errors	units
1	scale	13.169738	0.075010
2	sigma0	0.000000	0.000000
3	sigma1	0.000000	0.000000
4	sigma2	0.000000	0.000000
5	zero_shift	-4.165397	0.033715	µs

Start third round of minimization

In [34]:

job.fit()

job.fit()

Fitting successful
Duration: 11.88 s
Reduced chi: 5.57

Print free parameters after the third fitting

In [35]:

job.print_free_parameters()

job.print_free_parameters()

Out[35]:

	names	values	errors	units
1	scale	14.846289	0.046806
2	sigma0	-4.968327	0.923895
3	sigma1	66.704832	1.503366
4	sigma2	-10.512966	0.172826
5	zero_shift	-3.357013	0.034452	µs

Display the analysis chart after the third fitting

In [36]:

job.show_analysis_chart()

job.show_analysis_chart()